ABC is a triangle whose area is 50 cm square . Eand F are are midpoints of the sides.AB and AC respectively . Prove that EBCF is a trapezium and find its area
Answers
Area of EBCF trapezium = 37.5 cm²
Step-by-step explanation:
E & F are mid points of AB & AC
=> AE = BE = AB/2 & AF = CF = AC/2
=> BE/AB = 1/2 = CF/AC
Lets draw AD ⊥ BC , EM ⊥BC & FN⊥BC
Now in
Δ BEM & Δ BAD
∠B = ∠B ( common)
∠BME = ∠BDA = 90°
=> Δ BEM ≈ Δ BAD
=> BE/AB = EM/AD
Simialrly
Δ CFN ≈ Δ CAD
=> CF/AC = FN/AD
BE/AB = 1/2 = CF/AC
=> EM/AD = FN/AD
=> EM = FN
EM = FN ( EM & FN are perpincular to BC from EF)
=> EF ║BC
Hence EBCF is a trazpezium
ΔAEF ≈ ABC
ar (ΔAEF) / ar (ΔABC) = (AE/AB)² = 1/4
ar (ΔAEF) = 50/4
Area of EBCF trapezium = ar (ΔABC) - ar (ΔAEF) = 50 - 50/4
= 150/4
= 37.5 cm²
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